r^{- 1}

host and truncated satellite are

M_{h} (r_{o}) = 2 π A_{h} r_{o}^{2}, M_{s} = 2 π A_{s} r_{t}^{2} .

r_{t} = r_{o} [\frac{M _{s}}{( 3 - d l o g M _{h} / d l o g r _{o} ) M _{h} ( r _{o} )}]^{1/3} .

Since

d lo g M_{h} / d lo g r_{o} = 2

, substitution gives

r_{t}^{3} = r_{o}^{3} \frac{A _{s} r _{t}^{2}}{A _{h} r _{o}^{2}},

and hence

r_{t} = \frac{A _{s}}{A _{h}} r_{o} .

The assumption

A_{s} ≪ A_{h}

makes

r_{t} / r_{o} ≪ 1

, precisely the scale separation required by the local tidal approximation.

 Ancestors (10)

 Discussion (0)

There are no discussions about this article yet.

There are currently no matching articles.